Search results

Re: Several Variable Calculus \nabla \cdot \textbf{F}\text{ represents the divergence of the vector field} \text{What is this supposed to represent? }\textbf{F} \cdot \nabla

Re: Statistics \\X_1,\dots, X_n\text{ is a random sample from Unif}(0,\theta)\\ \text{Find the MLE }\hat{\theta}\text{ of }\theta \\ \text{After I write down the likelihood function }L(\theta; x_1,\dots,x_n) = \prod_{i=1}^n \frac1\theta = \frac{1}{\theta^n}\text{ I'm stumped..}

Re: MATH1131 help thread \text{Using the identity they supplied} \begin{align*}|z+3i|^2 &= (z+3i)\overline{(z+3i)}\\ &= (z+3i)(\overline{z}-3i)\\ &= z\overline{z} + 3i\overline{z} - 3iz - 9i^2\\ &= z\overline{z} - 3i(z-\overline{z}) + 9\end{align*}

Re: MATH1131 help thread \text{Their line one is wrong}\\ \text{It should read }4(z\overline{z}+3i(z-\overline{z})+9)=z\overline{z}\boxed{-3i(z-\overline{z})}+9

Re: Statistics Getting lost in what it means to converge in distribution to a constant X_n \stackrel{d}{\to} X\text{ is defined to mean}\\ \lim_{n\to \infty}F_{X_n}(x) = F_X(x) But I'm not seeing how FX(x) is allowed to be a constant. Because doesn't FX(x) technically have to satisfy these...

\int \sqrt[100]{\tan x}\,dx

Re: Several Variable Calculus My lecture slides. I haven't used a maths textbook before at uni. I'm just going to have to take it up with the lecturer

Re: Several Variable Calculus For our version, P and Q (as used above) have to be C1 on \Omega \cup \partial \Omega That was really the only condition given.

Re: Several Variable Calculus Couldn't find anything else though ___________ Not sure at all if this helps: \text{Q31: Use that result to find the area of the planar region enclosed by the astroid}\\ x^{\frac23}+y^{\frac23}=a^{\frac23}\text{ for }a>0

Re: Several Variable Calculus I don't want this question done just yet, I just want to know why the hint works \text{Show that for any planar region }\Omega\\ \text{area}(\Omega) = \frac{1}{2}\oint_{\partial \Omega}(x\, dy - y \, dx) \text{Hint: Apply Green's Theorem with }\boxed{P=-y,\quad...

Re: Several Variable Calculus Ohhhhhhh I see now, completely forgot about that!

Re: Several Variable Calculus Yep f(x) = \begin{cases}0& -\pi \le x \le 0\\ 1& 0 < x < \pi\end{cases} If we ensure that f(x + 2pi) = f(x) I can visually see why it fails to work, but I still can't figure out where to get started

Re: MATH1131 help thread You can always practice doing it the long way but very quickly (and because you're now at uni you can omit a few steps)

Re: Several Variable Calculus Sf(x) = \frac12 + \frac2\pi \sum_{k=1}^\infty \frac{\sin [(2k-1)x]}{2k-1} How would I show that this series does not converge uniformly? I don't think I can use the Weierstrass M-test for divergence \text{Or if I use the definition, I really just don't know how...

Re: Several Variable Calculus Oh my bad, I see now. That was foolish of me.

Re: Several Variable Calculus Hmm, not sure if I'm missing something but I think there's an x-cubed there. I don't think the original function is even? http://www.wolframalpha.com/input/?t=crmtb01&f=ob&i=integrate+1%2F2(1-6x%5E2%2B4x%5E3)+from+-1+to+1 Although when I split up the x^3 and the...

Re: Several Variable Calculus f:\mathbb{R}\to \mathbb{R},\, f(x) = 1-6x^2+4x^3\text{ for }0\le x \le 1 f(x+2)=f(x)\text{ and }f(-x)=f(x) \, \forall x\in \mathbb{R} Required: The Fourier series Sf(x). Hints: I found that f'(0) = f'(1) = 0 and f'''(x) = 24 \\\text{Deduced: }a_0[f] = -2, \...

Re: Several Variable Calculus To be honest, all I could really write out was the definition you provided. I realised I had to work with n> N \implies n^\alpha x^n(1-x) < \epsilon I'm not sure what should delete to deduce my N.

Re: Several Variable Calculus Got that part out. \text{Now how would I prove uniform convergence for }\alpha < 1?

Re: Several Variable Calculus \text{Prove (using the definition) that }f_n:[0,1]\to \mathbb{R}\\ f_n(x) = n^\alpha x^n(1-x)\to 0\text{ pointwise} \alpha \in \mathbb{R}\text{ is fixed} (Also ignore the previous question, even the lecturer agreed it was lacking information)